The survey above omits a number of views.17 Most prominent of these is that of Mach (1906). He accounts for thought experiments as the manipulation of instinctively gained raw experience by a few simple schemes, such as variations of the conditions that determine the result. For example, he considers (p. 138) the distance above the earth of a falling stone. If that distance is increased in thought to the height of the moon we would still expect the stone to fall in some diminished degree, suggesting that the moon, composed of many stones, also falls towards the earth. The difficulty with Mach's view is that it is readily assimilated to nearly all viewpoints. I see his raw experience as supplying premises for the arguments that implement the manipulations. Nersessian (1992, p. 292) sees much in common between Mach's and her view. Gendler (1998, p.415) calls on Mach for help in one stage of her account. Sorensen (1991) finds an evolutionary epistemology in Mach. So I am not sure how to categorize it.
Bishop (1999) has proposed a most ingenious demonstration of why thought experiments cannot be arguments. He reflects on Einstein's celebrated clock-in-the-box thought experiment which was conducted in a classical spacetime. Bohr replicated it in a relativistic spacetime and recovered a different outcome. It is the one thought experiment, Bishop urges, but must be reconstructed as two arguments; so thought experiments cannot be arguments. In my view, the difficulty is that Einstein and Bohr do have two different, but similar thought experiments; and they correspond to two different, but similar arguments. We can convert the two thought experiments into one by ignoring the different spacetimes of each. The different spacetime settings are then responsible for the different outcomes. If that is admissible, then the same stratagem works for the arguments. Ignoring premises pertaining to the spacetime setting, the two arguments proceed from the same experimental premises. They arrive at different results only because of the differences in the premises pertaining to spacetime setting.
Finally I also correct a persistent confusion concerning my view. Some (e.g. Gooding, 1992, p. 283 and Hacking, 1992, p. 303) report that I demand the argument in a thought experiment must be deductive; others suggest the argument must be symbolic (or so I have seen reported in a manuscript version of a paper); and others (Boorsboom et al., 2002) that the arguments must be derivations within some definite theory. A brief review of what I have written will show that none of these restrictions are a part of my view, which allows inductive and informal argumentation and premises from outside any fixed theory.18
I have defended my view that thought experiments in science are merely picturesque arguments. Their epistemic reach can always be replicated by an argument and this is best explained by their merely being arguments. I also urged that thought experiments can only be used reliably if they are governed by some sort of logic, even if of a very general kind, and proposed that the natural evolution of the literature in deductive and inductive logic would extract and codify the implicit logic of thought experiments. So thought experiments are arguments, but not because thought experimenters have sought to confine themselves to the modes in the existing literature on argumentation; it is because the literature on argumentation has adapted itself to thought experiments.
This argument view provides a natural home for an empiricist account of thought experiments. In so far as a thought experiment provides novel information about the world, that information was introduced as experientially based premises in the arguments. The argument view may not be the only view that can support an empiricist epistemology. I have surveyed other accounts above and at least constructivism, mental modeling and experimentalism may support an empiricist epistemology. However I have also urged that these accounts are merely variants of the argument view, in so far as they are viable, and that fact may already account for their hospitality to empiricism.19
Arthur, R. (1999) "On Thought Experiments as a priori Science," International Studies in the Philosophy of Science, 13, pp. 215-229.
Bishop, M. (1999) "Why Thought Experiments are not Arguments," Philosophy of Science, 66, pp. 534-41.
Boorsboom, G. Mellenbergh, G. and van Heerden, J. (2002) "Functional Thought Experiments," Synthese, 130, pp. 379-87.
Brown, J. (1991) The Laboratory of the Mind: Thought Experiments in the Natural Sciences. London: Routledge.
Brown, J. (1992) "Why Empiricism Won't Work." pp. 271-279 in Hull et al. (1992).
Brown, J. (1993) "Author's Response" (to Norton, 1993) Metascience, 3 (new series), pp. 38-40.
Brown, J. (manuscript) "Peeking into Plato's Heaven," Prepared for Philosophy of Science Association Biennial Meeting, 2002, Milwaukee, Wisconsin.
Gendler, T. Szabó (1998) "Galileo and the Indispensability of Scientific Thought Experiments," British Journal for the Philosophy of Science, 49, pp. 397-424.
Gooding, D. (1992) "What is Experimental about Thought Experiments?" pp. 280-90 in Hull, Forbes and Okruhlik (1992).
Häggqvist, S. (1996) Thought Experiments in Philosophy. Stockholm Studies in Philosophy 18. Stockholm: Almqvist & Wiksel International.
Hacking , I. (1992) "Do Thought Experiments Have a Life of their Own? Comments on James Brown, Nancy Nersessian and David Gooding," pp. 302-308 in Hull, Forbes and Okruhlik (1992).
Horowitz, T. and Massey, G. J. eds. (1991) Thought Experiments in Science and Philosophy. Savage, MD: Rowman and Littlefield.
Hull, D. Forbes, M. and Okruhlik, K.(eds.) (1992) PSA 1992: Proceedings of the 1992 Biennial Meeting of the Philosophy of Science Association. Volume 2. East Lansing, MI: Philosophy of Science Association 1993.
Johnson-Laird, P. N. (1989) "Mental Models" pp. 469-500 in M. Posner (ed.) Foundations of Cognitive Science. Cambrdige: MIT Press.
Klein, M. Kox, A. J., Renn, J. and Schulmann, R. (1993) The Collected Papers of Albert Einstein. Volume 3 The Swiss Years, 1909-1911. Princeton: Princeton University Press.
Kuhn, T. S. (1964) "A Function for Thought Experiments," L'Aventure de la Science, Mélanges Alexandre Koyré. Paris: Hermann, 1964. 2, pp. 307-34; reprinted in The Essential Tension: Selected Studies in Scientific Tradition and Change. Chicago: University of Chicago Press, 1977, pp. 240-65.
Kühne, Ulrich (2001) Die Methode der Gedankenexperimente: Untersuchung zur Rationalität naturwissenschaftler Theorienform. Manuscript.
Laymon, R. (1991) "Thought Experiments by Stevin, Mach and Gouy: Thought Experiments as Ideal Limits and as Semantic Domains," pp. 167-191 in Horowitz and Massey (1991).
Mach, E. (1906) "Über Gedankenexperimente," pp.183-200 in Erkenntnis und Irrtum. Skizzen zur Psychologie der Forschung.2nd, ed., Leipzig: Verlag von Johann Ambrosius, 1906; translated from the 5th ed. as "On Thought Experiments," pp. 134-47 in Knowledge and Error: Sketches on the Psychology of Enquiry trans. T. J. McCormack, Dordrecht: D. Reidel, 1976.
Mach, E. (1893) The Science of Mechanics: A Critical and Historical Account of its Development. 6th ed. trans. T. J. McCormack. La Salle, IL: Open Court,1960.
McAllister, J. (1996) "The Evidential Significance of Thought Experiment in Science," Studies in History and Philosophy of Science,27, pp. 233-50.
Nersessian, N. (1992) "In the Theoretician's Laboratory: Thought Experimenting as Mental Modeling," pp. 291-301 in Hull, Forbes and Okruhlik (1992).
Norton, J. D. (1991) "Thought Experiments in Einstein's Work." in Horowitz and Massey (1991), 129-148.
Norton, J. D. (1993) "Seeing the Laws of Nature," (Review of Brown, 1991) Metascience, 3 (new series), pp. 33-38.
Norton, J. D. (1996) "Are Thought Experiments Just What You Thought?" Canadian Journal of Philosophy, 26, pp. 333-66.
Norton, J. D. (manuscript) "On Thought Experiments: Is There More to the Argument?" Prepared for Philosophy of Science Association Biennial Meeting, 2002, Milwaukee, Wisconsin.
Palmieri, P. (forthcoming) "Mental Models in Galileo's Early Mathematization of Nature." Studies in History and Philosophy of Science.
Pais, A. (1982) "Subtle is the Lord…: The Science and Life of Albert Einstein. Clarendon: Oxford.
Sorabji, R. (1988) Matter, Space and Motion: Theories in Antiquity and their Sequel. London: Duckworth.
Sorensen, R. (1991) "Thought Experiments and the Epistemology of Laws," Canadian Journal of Philosophy, 22, pp. 15-44.
Sorensen, R. (1992) Thought Experiments. Oxford: Oxford Univ. Press.
Stachel, J. (1980) "Einstein and the Rigidly Rotating Disk," pp. 48-62 in D.Howard and J. Stachel (eds.) Einstein and the History of General Relativity: Einstein Studies Vol. 1. Boston: Birkhäuser, 1989.
1 I am grateful to Greg Frost and Wendy Parker for helpful comments and to Jim Brown for over fifteen years of stimulating debate.
2 Such was the case when D. C. Miller repeated the famous Michelson Morley experiment in 1921 and reported evidence of the motion of the earth through the ether. The result is immediately dismissed by anyone who holds to special relativity. However Einstein in addition suggested that the result could be due to tiny thermal gradients in the equipment. See Pais (1982, pp. 113-14).
3 A fourth pair that retains the theme of rotation is the thought experiment of Newton's bucket that favors absolute space. Mach's anti-thought experiment imagines the bucket walls to be made several leagues thick; it is usually interpreted as blocking Newton's claim. See Norton (1996, pp. 347-49), Mach (1893, p. 284). See also Norton (manuscript) for another thought experiment – anti thought experiment pair and for criticism of alternative epistemologies.
4 Simplicus, Phys. 467, 26-32 as quoted in Sorabji (1988, p.125).
5 See "Einstein on Length Contraction in the Theory of Relativity" pp. 478-80 in Klein et al. (1993).
6 The (minimum) power required to sustain the lift is just the kinetic energy of the air moved per unit time, that is P = mv2/2. So in this process the power is halved to (2m)(v/2)2/2 = mv2/(2x2) = P/2. Thus in the limit of the infinite rotor, no power is needed to sustain the lift L. "That must be how angels work. Wide wing spans."—Jeremy Butterfield.
7 In my original account (Norton, 1991), I required that:
Thought experiments are arguments which:
(i) posit hypothetical or counterfactual states of affairs, and
(ii) invoke particulars irrelevant to the generality of the conclusion.
where (i) and (ii) are conditions necessary for an argument to be a thought experiment, but not sufficient. The analysis of Norton (1991) was intended in part to investigate the ramifications of the existence of these necessary conditions.
8 Given condition (ii) above, that thought experiment arguments invoke particulars irrelevant to the generality of the conclusion, thesis (1a) entails that thought experiments may be eliminated from our discourse without loss of demonstrative power, although the actual arguments that replace them may well be harder to follow. This is the "elimination thesis" (Norton, 1991, p. 131).
9 A simple example is a famous thought experiment due to Mach (1893, p. 269). He had introduced a definition of equality of mass under which two masses are equal if they engender the same acceleration in each other when the masses interact. Is this notion of equality transitive, he asked. That is, if mass A equals mass B; and mass B equals mass C; then does mass A equal mass C? The thought experiment answers that it must. He imagines the three masses sliding frictionlessly on a ring. If mass A fails to equal mass C, then motion in one or other direction must self accelerate, violating vis viva (kinetic energy) conservation. In this outcome, there is no reform of a conceptual system. Instead Mach has demonstrated a simple result within his mechanics: his definition plus energy conservation yields the transitivity of equality of mass.
10 Boorsboom et al. (2002) analyse a single thought experiment in probability theory from a similar perspective. They urge that the thought experiment cannot be reconstructed as an argument since it is not a derivation within a theory but creates a conceptual framework for a theory in showing the viability of a frequentist conception of probability. I believe the objection fails since they too underestimate what an argument can achieve.
11 This seems to be the import of Gendler's (1998, Section 2.4) reflection that the Galilean thought experimenter ignores many logically admissible escapes from the reductio contradiction.
12 Gooding (1992, p. 285) writes: "Visual perception is crucial because the ability to visualize is necessary to most if not all thought experimentation."
13 Arthur (1999, p. 228) endorses a subsidiary epistemic power in visualizsation when he concludes "…I do not think thought experiments are simply reducible to arguments without epistemic loss…Thought experiments go beyond arguments in providing an easily visualizable— or…graspable— imaginative reconstruction of the phenomenon at issue."
14 That templates in logic can also be contingent is actually quite familiar. It is a contingent fact that "If something is human, then it is mortal." That fact licenses inferences as well. From "Socrates is human." we are licensed by it to infer to "Socrates is mortal."
15 More precisely, he refuses to reply with "direct denial" (p.214) and proceeds instead with a rather transparent evasion of the question. He offers a "parity thesis": "thought experiments are arguments if and only if experiments are arguments" and urges that, if we believe thought experiments are arguments, we must take the burden of proving that real experiments are arguments. What makes the evasion curious is that there seems no strong reason to accept the parity thesis. It is not even clear what it asserts. Does "[real] experiments are arguments" mean that they are entirely arguments, a claim that is obviously false? Or does it mean that real experiments contain some argumentation, a claim that would be easily sustained if we allow that the notion of experiment includes even some minimal interpretation of the raw data read by the experimenter?
16 For example, a thought experiment quickly establishes that the time reversibility of physical law is not directly expressed in the phenomena. The phenomena manifest a decided unidirectionality in time. To see this, we need only imagine that we locate a familiar process in a device capable of reversing its time order. If the device is large enough to host a banquet, we would find elegantly dressed diners regurgitating the content of their stomachs, chewing it back to pristine morsels and modestly conveying them back to their plates with their forks—a process compatible with the physical laws but otherwise never seen. The thought experiment does not employ a continuous approach to some ideal limit, such as the gradual elimination of friction. Indeed the thought experiment is more effective the more we avoid idealization, that is, the more realistic we make the processes subject to time reversal.
17 See also Kuehne (2001) which includes an account of Oersted's views on thought experimentation. I also pass over McAllister's (1996) claim that thought experimentation is evidentially inert unless one accepts a Galilean doctrine of phenomena, since the view does not supply an alternative epistemology but explores the foundations of all epistemologies of thought experiments. For criticism of his view, see Norton (manuscript).
18 Häggqvist (1996, pp. 89-91) criticizes me precisely because he finds me too lenient in admitting inductive inference into the treatment of thought experiments as arguments.
19 What is my resolution of the thought experiment-anti thought experiment pairs? In the case of the rotating disk, the anti-thought experiment fails. A rigid ring cannot be set into rotation preserving rigidity; it would shatter exactly because of the Lorentz contraction. In the case of the infinite rotor, the assumption that is false is that the limit of infinitely many doublings (of the moving rotor) produces a physically admissible system. An air current is required for lift and that is absent in the limit. Sometimes limits can yield nonsense.